curve #1133

y² = x³ − x² − 2357260x − 257373158

a-invariants: [0, -1, 0, -2357260, -257373158]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 7727548608960
discriminant (Δ): 809515002817537944000
Faltings height: 2.7022
naive height: 55.6326
primes of bad reduction: 2, 3, 5, 17, 113, 769, 5449
regulator: 26835.837950067874948551723670466578955882219651218
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:05 UTC
last updated: 2026-09-23 21:37:05 UTC

Witness: 6 independent points log in to add more points →

(-181, 12780)
(-321, 21590)
(-801, -33410)
(1659, -19880)
(-579/4, 71905/8)
(1887, -44834)

Commentary

Obtained by computing a rational isogeny from curve#16 and mapping all 6 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.

last edited by David Renshaw at 2026-09-23 21:37:05 UTC · history